The student will calculate a 90% confidence interval using the given data.
The student will determine the relationship between the confidence level and the percentage of constructed intervals that contain the population mean.
Given:
Heights of 100 women (in inches)
59.4
71.6
69.3
65.0
62.9
66.5
61.7
55.2
67.5
67.2
63.8
62.9
63.0
63.9
68.7
65.5
61.9
69.6
58.7
63.4
61.8
60.6
69.8
60.0
64.9
66.1
66.8
60.6
65.6
63.8
61.3
59.2
64.1
59.3
64.9
62.4
63.5
60.9
63.3
66.3
61.5
64.3
62.9
60.6
63.8
58.8
64.9
65.7
62.5
70.9
62.9
63.1
62.2
58.7
64.7
66.0
60.5
64.7
65.4
60.2
65.0
64.1
61.1
65.3
64.6
59.2
61.4
62.0
63.5
61.4
65.5
62.3
65.5
64.7
58.8
66.1
64.9
66.9
57.9
69.8
58.5
63.4
69.2
65.9
62.2
60.0
58.1
62.5
62.4
59.1
66.4
61.2
60.4
58.7
66.7
67.5
63.2
56.6
67.7
62.5
[link] lists the heights of 100 women. Use a random number generator to select ten data values randomly.
Calculate the sample mean and the sample standard deviation. Assume that the population standard deviation is known to be 3.3 inches. With these values, construct a 90% confidence interval for your sample of ten values. Write the confidence interval you obtained in the first space of
[link] .
Now write your confidence interval on the board. As others in the class write their confidence intervals on the board, copy them into
[link] .
90% confidence intervals
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Discussion questions
The actual population mean for the 100 heights given
[link] is
μ = 63.4. Using the class listing of confidence intervals, count how many of them contain the population mean
μ ; i.e., for how many intervals does the value of
μ lie between the endpoints of the confidence interval?
Divide this number by the total number of confidence intervals generated by the class to determine the percent of confidence intervals that contains the mean
μ . Write this percent here: _____________.
Is the percent of confidence intervals that contain the population mean
μ close to 90%?
Suppose we had generated 100 confidence intervals. What do you think would happen to the percent of confidence intervals that contained the population mean?
When we construct a 90% confidence interval, we say that we are
90% confident that the true population mean lies within the confidence interval. Using complete sentences, explain what we mean by this phrase.
Some students think that a 90% confidence interval contains 90% of the data. Use the list of data given (the heights of women) and count how many of the data values lie within the confidence interval that you generated based on that data. How many of the 100 data values lie within your confidence interval? What percent is this? Is this percent close to 90%?
Explain why it does not make sense to count data values that lie in a confidence interval. Think about the random variable that is being used in the problem.
Suppose you obtained the heights of ten women and calculated a confidence interval from this information. Without knowing the population mean
μ , would you have any way of knowing
for certain if your interval actually contained the value of
μ ? Explain.
Questions & Answers
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
In this morden time nanotechnology used in many field .
1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc
2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc
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and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change .
maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
Source:
OpenStax, Statistics i - math1020 - red river college - version 2015 revision a - draft 2015-10-24. OpenStax CNX. Oct 24, 2015 Download for free at http://legacy.cnx.org/content/col11891/1.8
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